Add dfa.py (keon#606)

* fix the comment on line 33 (left->right)

* add DFA.py

* Update README.md

* Update merge_sort.py

* Create test_automata.py

* Update test_automata.py

* Update DFA.py

* Update test_automata.py

* Update test_automata.py

* Create __init__.py

* Update DFA.py

* Update test_automata.py

* Update test_automata.py

* Update test_automata.py

README.md

@@ -71,6 +71,8 @@ If you want to uninstall algorithms, it is as simple as:
     - [two_sum](algorithms/arrays/two_sum.py)
     - [move_zeros](algorithms/arrays/move_zeros.py)
     - [n_sum](algorithms/arrays/n_sum.py)
+- [automata](algorithms/automata)
+    - [DFA](algorithms/automata/DFA.py)
 - [backtrack](algorithms/backtrack)
     - [general_solution.md](algorithms/backtrack/)
     - [add_operators](algorithms/backtrack/add_operators.py)

algorithms/automata/DFA.py

@@ -0,0 +1,18 @@
+def DFA(transitions, start, final, string):
+
+    num = len(string)
+    num_final = len(final)
+    cur = start
+
+    for i in range (num):
+
+        if transitions[cur][string[i]] == None:
+            return False
+        else:
+            cur = transitions[cur][string[i]]
+
+    for i in range (num_final):
+        if cur == final[i]:
+            return True
+    return False
+

algorithms/automata/__init__.py

@@ -0,0 +1 @@
+from .DFA import *

tests/test_automata.py

@@ -0,0 +1,48 @@
+from algorithms.automata import DFA
+
+
+import unittest
+
+
+class TestDFA(unittest.TestCase):
+    def test_DFA(self):
+
+        transitions = {
+            'a': {'1': 'a', '0': 'b'},
+            'b': {'1': 'b', '0': 'a'}
+        }
+
+        final=['a']
+        start = 'a'
+
+        self.assertEqual(False, DFA(transitions, start, final, "000111100"))
+        self.assertEqual(True, DFA(transitions, start, final, "111000011"))
+
+        transitions1 = {
+            '0': {'0': '1', '1': '0'},
+            '1': {'0': '2', '1': '0'},
+            '2': {'0': '2', '1': '3'},
+            '3': {'0': '3', '1': '3'}
+        }    
+
+        final1 = ['0', '1', '2']
+        start1 = '0'
+
+        self.assertEqual(False, DFA(transitions1, start1, final1, "0001111"))
+        self.assertEqual(True, DFA(transitions1, start1, final1, "01010101"))
+
+        transitions2 = {
+            '0': {'a': '0', 'b': '1'},
+            '1': {'a': '0', 'b': '2'},
+            '2': {'a': '3', 'b': '2'},
+            '3': {'a': '3', 'b': '3'}
+        }
+
+        final2=['3']
+        start2 = '0'
+
+        self.assertEqual(False, DFA(transitions2, start2, final2, "aaabbb"))
+        self.assertEqual(True, DFA(transitions2, start2, final2, "baabba"))
+
+if __name__ == '__main__':
+    unittest.main()